Table 1. Definition of new variables—Chern sector and pseudospin, from the valley and sublattice degrees of freedom.

Actions of symmetries on the internal indices are shown on the right, in both set of variables. In addition, the independent pseudospin rotations in the Chern sectors are generated by the ηP_± where the projectors $P_{\pm }=\frac{1}{2}(1\pm {\mathrm{\gamma }}_z)$ single out a specific Chern sector.

From valley/sublattice to Chern/pseudospin
(τ, σ) → (γ, η)
γ = (γx, γy, γz) = (σx, σyτz, σzτz)
η = (ηx, ηy, ηz) = (σxτx, σxτy, τz)
Basis
Valley	τz = K/K′
Sublattice	σz = A/B
Chern sector	γz = σzτz = + /−
Pseudospin	ηz = τz = ↑ps/↓ps
Symmetries
Symm	(τ, σ) basis	(γ, η) basis
T	τxK	γxηxK
C2	σxτx	ηx
UV(1)	eiϕτz	eiϕηz